A result due to Füredi and Komlós allows us to analyze the limiting behavior of polynomials in \(a_1, a_2, \ldots , a_n\) . Suppose \(A_n\)  is an \(n\times n\)  real symmetric matrix with bounded entries. Moreover, we assume the entries of \(A_n\) , modulo the constraint \(\xi _{ij}=\xi _{ji}\) , are independent. Let \(\mu =\mathbb {E}\xi _{ij}>0\)  denote the common mean of the upper-triangular entries and let \(\sigma ^2=\mathbb {E}(\xi _{ij}-\mu )^2\)  denote their common variance. Furthermore, suppose the diagonal entries share a common mean, \(\nu =\mathbb {E}\xi _{ii}\) . Füredi and Komlós [1]} show that the distribution of the largest eigenvalue \(\lambda _1\)  of \(A_n\)  can be approximated in order \(n^{-1/2}\)  by a normal distribution with mean \((n-1)\mu +\nu +\sigma ^2/\mu \)  and variance \(2\sigma ^2\) . Moreover, with high probability (w.h.p.) we have
\(|\lambda _i|<\sigma \sqrt{n}+O(n^{1/3}\log n)\) 
